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Miscellaneous Aspects of Machine Learning/Representation Learning

Yibo Jiang, Bryon Aragam, Victor Veitch

Machine learning tools often rely on embedding text as vectors of real numbers.In this paper, we study how the semantic structure of language is encoded in the algebraic structure of such embeddings.Specifically, we look at a notion of "semantic independence" capturing the idea that, e.g., "eggplant" and "tomato" are independent given "vegetable". Although such examples are intuitive, it is difficult to formalize such a notion of semantic independence. The key observation here is that any sensible formalization should obey a set of so-called independence axioms, and thus any algebraic encoding of this structure should also obey these axioms. This leads us naturally to use partial orthogonality as the relevant algebraic structure. We develop theory and methods that allow us to demonstrate that partial orthogonality does indeed capture semantic independence.Complementary to this, we also introduce the concept of independence preserving embeddings where embeddings preserve the conditional independence structures of a distribution, and we prove the existence of such embeddings and approximations to them.

Miscellaneous Aspects of Machine Learning/Causality

Yibo Jiang, Bryon Aragam

We establish conditions under which latent causal graphs are nonparametrically identifiable and can be reconstructed from unknown interventions in the latent space. Our primary focus is the identification of the latent structure in measurement models without parametric assumptions such as linearity or Gaussianity. Moreover, we do not assume the number of hidden variables is known, and we show that at most one unknown intervention per hidden variable is needed. This extends a recent line of work on learning causal representations from observations and interventions. The proofs are constructive and introduce two new graphical concepts---_imaginary subsets_ and _isolated edges_---that may be useful in their own right. As a matter of independent interest, the proofs also involve a novel characterization of the limits of edge orientations within the equivalence class of DAGs induced by _unknown_ interventions. These are the first results to characterize the conditions under which causal representations are identifiable without making any parametric assumptions in a general setting with unknown interventions and without faithfulness.

Miscellaneous Aspects of Machine Learning/Transfer, Multitask and Meta-learning

Parker Knight, Rui Duan

Multi-task learning has emerged as a powerful machine learning paradigm for integrating data from multiple sources, leveraging similarities between tasks to improve overall model performance. However, the application of multi-task learning to real-world settings is hindered by data-sharing constraints, especially in healthcare settings. To address this challenge, we propose a flexible multi-task learning framework utilizing summary statistics from various sources. Additionally, we present an adaptive parameter selection approach based on a variant of Lepski's method, allowing for data-driven tuning parameter selection when only summary statistics are accessible. Our systematic non-asymptotic analysis characterizes the performance of the proposed methods under various regimes of the source datasets' sample complexity and overlap. We demonstrate our theoretical findings and the performance of the method through extensive simulations. This work offers a more flexible tool for training related models across various domains, with practical implications in genetic risk prediction and many other fields.

Miscellaneous Aspects of Machine Learning/Kernel methods

Ethan Epperly, Elvira Moreno

This paper presents new quadrature rules for functions in a reproducing kernel Hilbert space using nodes drawn by a sampling algorithm known as randomly pivoted Cholesky. The resulting computational procedure compares favorably to previous kernel quadrature methods, which either achieve low accuracy or require solving a computationally challenging sampling problem. Theoretical and numerical results show that randomly pivoted Cholesky is fast and achieves comparable quadrature error rates to more computationally expensive quadrature schemes based on continuous volume sampling, thinning, and recombination. Randomly pivoted Cholesky is easily adapted to complicated geometries with arbitrary kernels, unlocking new potential for kernel quadrature.

Reinforcement Learning

Gen Li, Wenhao Zhan, Jason Lee, Yuejie Chi, Yuxin Chen

This paper studies tabular reinforcement learning (RL) in the hybrid setting, which assumes access to both an offline dataset and online interactions with the unknown environment. A central question boils down to how to efficiently utilize online data to strengthen and complement the offline dataset and enable effective policy fine-tuning. Leveraging recent advances in reward-agnostic exploration and offline RL, we design a three-stage hybrid RL algorithm that beats the best of both worlds --- pure offline RL and pure online RL --- in terms of sample complexities. The proposed algorithm does not require any reward information during data collection. Our theory is developed based on a new notion called **single-policy partial concentrability**, which captures the trade-off between distribution mismatch and miscoverage and guides the interplay between offline and online data.

Miscellaneous Aspects of Machine Learning/Unsupervised and Semi-supervised Learning

Qing Su, Anton Netchaev, Hai Li, Shihao Ji

Current self-supervised learning (SSL) methods (e.g., SimCLR, DINO, VICReg, MOCOv3) target primarily on representations at instance level and do not generalize well to dense prediction tasks, such as object detection and segmentation. Towards aligning SSL with dense predictions, this paper demonstrates for the first time the underlying mean-shift clustering process of Vision Transformers (ViT), which aligns well with natural image semantics (e.g., a world of objects and stuffs). By employing transformer for joint embedding and clustering, we propose a bi-level feature clustering SSL method, coined Feature-Level Self-supervised Learning (FLSL). We present the formal definition of the FLSL problem and construct the objectives from the mean-shift and k-means perspectives. We show that FLSL promotes remarkable semantic cluster representations and learns an embedding scheme amenable to intra-view and inter-view feature clustering. Experiments show that FLSL yields significant improvements in dense prediction tasks, achieving 44.9 (+2.8)% AP and 46.5% AP in object detection, as well as 40.8 (+2.3)% AP and 42.1% AP in instance segmentation on MS-COCO, using Mask R-CNN with ViT-S/16 and ViT-S/8 as backbone, respectively. FLSL consistently outperforms existing SSL methods across additional benchmarks, including UAV object detection on UAVDT, and video instance segmentation on DAVIS 2017. We conclude by presenting visualization and various ablation studies to better understand the success of FLSL. The source code is available at https://github.com/ISL-CV/FLSL.

Miscellaneous Aspects of Machine Learning/Transfer, Multitask and Meta-learning

Gwen Legate, Nicolas Bernier, Lucas Page-Caccia, Edouard Oyallon, Eugene Belilovsky

Federated Learning (FL) is an emerging paradigm that allows a model to be trained across a number of participants without sharing data. Recent works have begun to consider the effects of using pre-trained models as an initialization point for existing FL algorithms; however, these approaches ignore the vast body of efficient transfer learning literature from the centralized learning setting. Here we revisit the problem of FL from a pre-trained model considered in prior work and expand it to a set of computer vision transfer learning problems. We first observe that simply fitting a linear classification head can be efficient in many cases. We then show that in the FL setting, fitting a classifier using the Nearest Class Means (NCM) can be done exactly and orders of magnitude more efficiently than existing proposals, while obtaining strong performance. Finally, we demonstrate that using a two-stage approach of obtaining the classifier and then fine-tuning the model can yield rapid convergence and improved generalization in the federated setting. We demonstrate the potential our method has to reduce communication and compute costs while achieving better model performance.

Miscellaneous Aspects of Machine Learning/General Machine Learning Techniques

Guy Blanc, Jane Lange, Chirag Pabbaraju, Colin Sullivan, Li-Yang Tan, Mo Tiwari

We propose a simple generalization of standard and empirically successful decision tree learning algorithms such as ID3, C4.5, and CART. These algorithms, which have been central to machine learning for decades, are greedy in nature: they grow a decision tree by iteratively splitting on the best attribute. Our algorithm, Top-$k$, considers the $k$ best attributes as possible splits instead of just the single best attribute. We demonstrate, theoretically and empirically, the power of this simple generalization. We first prove a greediness hierarchy theorem showing that for every $k\in \mathbb{N}$, Top-$(k+1)$ can be dramatically more powerful than Top-$k$: there are data distributions for which the former achieves accuracy $1-\epsilon$, whereas the latter only achieves accuracy $\frac{1}{2}+\epsilon$. We then show, through extensive experiments, that Top-$k$ outperforms the two main approaches to decision tree learning: classic greedy algorithms and more recent ``optimal decision tree'' algorithms. On one hand, Top-$k$ consistently enjoys significant accuracy gains over greedy algorithms across a wide range of benchmarks. On the other hand, Top-$k$ is markedly more scalable than optimal decision tree algorithms and is able to handle dataset and feature set sizes that remain far beyond the reach of these algorithms. The code to reproduce our results is available at https://github.com/SullivanC19/pydl8.5-topk.

Miscellaneous Aspects of Machine Learning/Everything Else

Yan-Shuo Liang, Wu-Jun Li

Continual learning requires the model to learn multiple tasks in a sequential order. To perform continual learning, the model must possess the abilities to maintain performance on old tasks (stability) and adapt itself to learn new tasks (plasticity). Task-agnostic problem in continual learning is a challenging problem, in which task identities are not available in the inference stage and hence the model must learn to distinguish all the classes in all the tasks. In task-agnostic problem, the model needs to learn two new objectives for learning a new task, including distinguishing new classes from old classes and distinguishing between different new classes. For task-agnostic problem, replay-based methods are commonly used. These methods update the model with both saved old samples and new samples for continual learning. Most existing replay-based methods mix the two objectives in task-agnostic problem together, inhibiting the models from achieving a good trade-off between stability and plasticity. In this paper, we propose a simple yet effective method, called loss decoupling (LODE), for task-agnostic continual learning. LODE separates the two objectives for the new task by decoupling the loss of the new task. As a result, LODE can assign different weights for different objectives, which provides a way to obtain a better trade-off between stability and plasticity than those methods with coupled loss. Experiments show that LODE can outperform existing state-of-the-art replay-based methods on multiple continual learning datasets.

Miscellaneous Aspects of Machine Learning

Jun-Yi Hang, Min-Ling Zhang

In partial multi-label learning (PML), each training example is associated with a set of candidate labels, among which only some labels are valid. As a common strategy to tackle PML problem, disambiguation aims to recover the ground-truth labeling information from such inaccurate annotations. However, existing approaches mainly rely on heuristics or ad-hoc rules to disambiguate candidate labels, which may not be universal enough in complicated real-world scenarios. To provide a principled way for disambiguation, we make a first attempt to explore the probabilistic graphical model for PML problem, where a directed graph is tailored to infer latent ground-truth labeling information from the generative process of partial multi-label data. Under the framework of stochastic gradient variational Bayes, a unified variational lower bound is derived for this graphical model, which is further relaxed probabilistically so that the desired prediction model can be induced with simultaneously identified ground-truth labeling information. Comprehensive experiments on multiple synthetic and real-world data sets show that our approach outperforms the state-of-the-art counterparts.

Miscellaneous Aspects of Machine Learning/Representation Learning

Haoyi Duan, Yan Xia, Zhou Mingze, Li Tang, Jieming Zhu, Zhou Zhao

In recent years, the deployment of large-scale pre-trained models in audio-visual downstream tasks has yielded remarkable outcomes. However, these models, primarily trained on single-modality unconstrained datasets, still encounter challenges in feature extraction for multi-modal tasks, leading to suboptimal performance. This limitation arises due to the introduction of irrelevant modality-specific information during encoding, which adversely affects the performance of downstream tasks. To address this challenge, this paper proposes a novel Dual-Guided Spatial-Channel-Temporal (DG-SCT) attention mechanism. This mechanism leverages audio and visual modalities as soft prompts to dynamically adjust the parameters of pre-trained models based on the current multi-modal input features. Specifically, the DG-SCT module incorporates trainable cross-modal interaction layers into pre-trained audio-visual encoders, allowing adaptive extraction of crucial information from the current modality across spatial, channel, and temporal dimensions, while preserving the frozen parameters of large-scale pre-trained models. Experimental evaluations demonstrate that our proposed model achieves state-of-the-art results across multiple downstream tasks, including AVE, AVVP, AVS, and AVQA. Furthermore, our model exhibits promising performance in challenging few-shot and zero-shot scenarios. The source code and pre-trained models are available at https://github.com/haoyi-duan/DG-SCT.

Miscellaneous Aspects of Machine Learning/Scalable Algorithms

Philip Sun, David Simcha, Dave Dopson, Ruiqi Guo, Sanjiv Kumar

This paper introduces SOAR: **S**pilling with **O**rthogonality-**A**mplified **R**esiduals, a novel data indexing technique for approximate nearest neighbor (ANN) search. SOAR extends upon previous approaches to ANN search, such as spill trees, that utilize multiple redundant representations while partitioning the data to reduce the probability of missing a nearest neighbor during search. Rather than training and computing these redundant representations independently, however, SOAR uses an *orthogonality-amplified residual* loss, which optimizes each representation to compensate for cases where other representations perform poorly. This drastically improves the overall index quality, resulting in state-of-the-art ANN benchmark performance while maintaining fast indexing times and low memory consumption.

Miscellaneous Aspects of Machine Learning/Kernel methods

Patric Bonnier, Harald Oberhauser, Zoltan Szabo

In $\mathbb{R}^d$, it is well-known that cumulants provide an alternative to moments that can achieve the same goals with numerous benefits such as lower variance estimators. In this paper we extend cumulants to reproducing kernel Hilbert spaces (RKHS) using tools from tensor algebras and show that they are computationally tractable by a kernel trick. These kernelized cumulants provide a new set of all-purpose statistics; the classical maximum mean discrepancy and Hilbert-Schmidt independence criterion arise as the degree one objects in our general construction. We argue both theoretically and empirically (on synthetic, environmental, and traffic data analysis) that going beyond degree one has several advantages and can be achieved with the same computational complexity and minimal overhead in our experiments.

Miscellaneous Aspects of Machine Learning/Causality

Amir Feder, Yoav Wald, Claudia Shi, Suchi Saria, David Blei

The reliance of text classifiers on spurious correlations can lead to poor generalization at deployment, raising concerns about their use in safety-critical domains such as healthcare. In this work, we propose to use counterfactual data augmentation, guided by knowledge of the causal structure of the data, to simulate interventions on spurious features and to learn more robust text classifiers. We show that this strategy is appropriate in prediction problems where the label is spuriously correlated with an attribute. Under the assumptions of such problems, we discuss the favorable sample complexity of counterfactual data augmentation, compared to importance re-weighting. Pragmatically, we match examples using auxiliary data, based on diff-in-diff methodology, and use a large language model (LLM) to represent a conditional probability of text. Through extensive experimentation on learning caregiver-invariant predictors of clinical diagnoses from medical narratives and on semi-synthetic data, we demonstrate that our method for simulating interventions improves out-of-distribution (OOD) accuracy compared to baseline invariant learning algorithms.

Miscellaneous Aspects of Machine Learning/Unsupervised and Semi-supervised Learning

Lei Zhang, Ji-Fu Li, Wei Wang

Semi-Supervised Domain Generalization (SSDG) aims to learn a model that is generalizable to an unseen target domain with only a few labels, and most existing SSDG methods assume that unlabeled training and testing samples are all known classes. However, a more realistic scenario is that known classes may be mixed with some unknown classes in unlabeled training and testing data. To deal with such a scenario, we propose the Class-Wise Adaptive Exploration and Exploitation (CWAEE) method. In particular, we explore unlabeled training data by using one-vs-rest classifiers and class-wise adaptive thresholds to detect known and unknown classes, and exploit them by adopting consistency regularization on augmented samples based on Fourier Transformation to improve the unseen domain generalization. The experiments conducted on real-world datasets verify the effectiveness and superiority of our method.

Miscellaneous Aspects of Machine Learning/Kernel methods

Mathieu Chalvidal, Thomas Serre, Rufin VanRullen

Research in statistical learning has polarized into two general approaches to perform regression analysis: Transductive methods construct estimates directly based on exemplar data using generic relational principles which might suffer from the curse of dimensionality. Conversely, inductive methods can potentially fit highly complex functions at the cost of compute-intensive solution searches. In this work, we leverage the theory of vector-valued Reproducing Kernel Banach Spaces (RKBS) to propose a hybrid approach: We show that transductive regression systems can be meta-learned with gradient descent to form efficient _in-context_ neural approximators of function defined over both finite and infinite-dimensional spaces (operator regression). Once trained, our _Transducer_ can almost instantaneously capture new functional relationships and produce original image estimates, given a few pairs of input and output examples. We demonstrate the benefit of our meta-learned transductive approach to model physical systems influenced by varying external factors with little data at a fraction of the usual deep learning training costs for partial differential equations and climate modeling applications.

Miscellaneous Aspects of Machine Learning/Everything Else

Felipe Maia Polo, Yuekai Sun, Moulinath Banerjee

Conditional independence (CI) testing is a fundamental and challenging task in modern statistics and machine learning. Many modern methods for CI testing rely on powerful supervised learning methods to learn regression functions or Bayes predictors as an intermediate step; we refer to this class of tests as regression-based tests. Although these methods are guaranteed to control Type-I error when the supervised learning methods accurately estimate the regression functions or Bayes predictors of interest, their behavior is less understood when they fail due to misspecified inductive biases; in other words, when the employed models are not flexible enough or when the training algorithm does not induce the desired predictors. Then, we study the performance of regression-based CI tests under misspecified inductive biases. Namely, we propose new approximations or upper bounds for the testing errors of three regression-based tests that depend on misspecification errors. Moreover, we introduce the Rao-Blackwellized Predictor Test (RBPT), a regression-based CI test robust against misspecified inductive biases. Finally, we conduct experiments with artificial and real data, showcasing the usefulness of our theory and methods.

Miscellaneous Aspects of Machine Learning/Representation Learning

Shashanka Venkataramanan, Ewa Kijak, laurent amsaleg, Yannis Avrithis

Mixup refers to interpolation-based data augmentation, originally motivated as a way to go beyond empirical risk minimization (ERM). Its extensions mostly focus on the definition of interpolation and the space (input or feature) where it takes place, while the augmentation process itself is less studied. In most methods, the number of generated examples is limited to the mini-batch size and the number of examples being interpolated is limited to two (pairs), in the input space.We make progress in this direction by introducing MultiMix, which generates an arbitrarily large number of interpolated examples beyond the mini-batch size and interpolates the entire mini-batch in the embedding space. Effectively, we sample on the entire convex hull of the mini-batch rather than along linear segments between pairs of examples.On sequence data, we further extend to Dense MultiMix. We densely interpolate features and target labels at each spatial location and also apply the loss densely. To mitigate the lack of dense labels, we inherit labels from examples and weight interpolation factors by attention as a measure of confidence.Overall, we increase the number of loss terms per mini-batch by orders of magnitude at little additional cost. This is only possible because of interpolating in the embedding space. We empirically show that our solutions yield significant improvement over state-of-the-art mixup methods on four different benchmarks, despite interpolation being only linear. By analyzing the embedding space, we show that the classes are more tightly clustered and uniformly spread over the embedding space, thereby explaining the improved behavior.

Miscellaneous Aspects of Machine Learning/General Machine Learning Techniques

Paul Mineiro, Steven Howard

Estimation of a complete univariate distribution from a sequence of observations is a useful primitive for both manual and automated decision making. This problem has received extensive attention in the i.i.d. setting, but the arbitrary data dependent setting remains largely unaddressed. We present computationally felicitous time-uniform and value-uniform bounds on the CDF of the running averaged conditional distribution of a sequence of real-valued random variables. Consistent with known impossibility results, our CDF bounds are always valid but sometimes trivial when the instance is too hard, and we give an instance-dependent convergence guarantee. The importance-weighted extension is appropriate for estimating complete counterfactual distributions of rewards given data from a randomized experiment, e.g., from an A/B test or a contextual bandit.

Miscellaneous Aspects of Machine Learning/Causality

Adam Li, Amin Jaber, Elias Bareinboim

A fundamental problem in many sciences is the learning of causal structure underlying a system, typically through observation and experimentation. Commonly, one even collects data across multiple domains, such as gene sequencing from different labs, or neural recordings from different species. Although there exist methods for learning the equivalence class of causal diagrams from observational and experimental data, they are meant to operate in a single domain. In this paper, we develop a fundamental approach to structure learning in non-Markovian systems (i.e. when there exist latent confounders) leveraging observational and interventional data collected from multiple domains. Specifically, we start by showing that learning from observational data in multiple domains is equivalent to learning from interventional data with unknown targets in a single domain. But there are also subtleties when considering observational and experimental data. Using causal invariances derived from do-calculus, we define a property called S-Markov that connects interventional distributions from multiple-domains to graphical criteria on a selection diagram. Leveraging the S-Markov property, we introduce a new constraint-based causal discovery algorithm, S-FCI, that can learn from observational and interventional data from different domains. We prove that the algorithm is sound and subsumes existing constraint-based causal discovery algorithms.